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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 623 · 40 questions
TalentJR

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

NameDateTime takenScore ___ / 40
  1. 1.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  2. 2.What is the midpoint of the line joining (5, 0) and (9, 10)? (a) (7, 5) (b) (2, 5) (c) (14, 10) (d) (5, 7)
  3. 3.What is the midpoint of the line joining (0, 6) and (4, 8)? (a) (4, 14) (b) (2, 7) (c) (2, 1) (d) (7, 2)
  4. 4.What is the midpoint of the line joining (5, 13) and (17, 9)? (a) (22, 22) (b) (11, 11) (c) (12, 11) (d) (6, 2)
  5. 5.What is the distance between the points (5, 17) and (17, 1)? (a) 400 (b) 28 (c) 20 (d) 21
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  7. 7.What is the distance between the points (8, 14) and (16, 8)? (a) 100 (b) 11 (c) 14 (d) 10
  8. 8.What is the distance between the points (2, 5) and (6, 8)? (a) 25 (b) 7 (c) 5 (d) 6
  9. 9.What is the midpoint of the line joining (6, 7) and (14, 1)? (a) (4, 10) (b) (20, 8) (c) (10, 4) (d) (4, 3)
  10. 10.What is the midpoint of the line joining (6, 10) and (12, 12)? (a) (9, 11) (b) (3, 1) (c) (11, 9) (d) (18, 22)
  11. 11.In which quadrant does the point (4, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  12. 12.In which quadrant does the point (3, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  13. 13.What is the distance between the points (6, 6) and (18, 15)? (a) 225 (b) 21 (c) 16 (d) 15
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  15. 15.What is the midpoint of the line joining (5, 0) and (13, 8)? (a) (4, 9) (b) (4, 4) (c) (9, 4) (d) (18, 8)
  16. 16.What is the midpoint of the line joining (9, 2) and (19, 8)? (a) (5, 14) (b) (14, 5) (c) (5, 3) (d) (28, 10)
  17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  19. 19.What is the distance between the points (2, 13) and (18, 1)? (a) 21 (b) 20 (c) 400 (d) 28
  20. 20.What is the distance between the points (6, 0) and (9, 4)? (a) 5 (b) 6 (c) 25 (d) 7
  21. 21.In which quadrant does the point (6, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  22. 22.What is the midpoint of the line joining (1, 14) and (5, 10)? (a) (12, 3) (b) (2, 2) (c) (3, 12) (d) (6, 24)
  23. 23.What is the midpoint of the line joining (6, 7) and (8, 11)? (a) (7, 9) (b) (14, 18) (c) (1, 2) (d) (9, 7)
  24. 24.What is the distance between the points (8, 5) and (14, 13)? (a) 14 (b) 100 (c) 11 (d) 10
  25. 25.What is the midpoint of the line joining (6, 9) and (8, 1)? (a) (1, 4) (b) (14, 10) (c) (5, 7) (d) (7, 5)
  26. 26.What is the midpoint of the line joining (5, 9) and (11, 13)? (a) (11, 8) (b) (3, 2) (c) (8, 11) (d) (16, 22)
  27. 27.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.In which quadrant does the point (−8, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  29. 29.What is the distance between the points (2, 7) and (6, 10)? (a) 25 (b) 6 (c) 5 (d) 7
  30. 30.What is the midpoint of the line joining (7, 9) and (17, 1)? (a) (12, 5) (b) (5, 4) (c) (24, 10) (d) (5, 12)
  31. 31.In which quadrant does the point (−3, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  34. 34.What is the distance between the points (8, 10) and (20, 1)? (a) 21 (b) 16 (c) 15 (d) 225
  35. 35.What is the distance between the points (7, 6) and (15, 21)? (a) 17 (b) 23 (c) 18 (d) 289
  36. 36.What is the midpoint of the line joining (3, 22) and (5, 10)? (a) (8, 32) (b) (4, 16) (c) (1, 6) (d) (16, 4)
  37. 37.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  38. 38.What is the midpoint of the line joining (7, 9) and (9, 15)? (a) (12, 8) (b) (8, 12) (c) (1, 3) (d) (16, 24)
  39. 39.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (2, 17) and (14, 8)? (a) 225 (b) 15 (c) 21 (d) 16

Answer key

  1. 13
  2. (7, 5)
  3. (2, 7)
  4. (11, 11)
  5. 20
  6. 17
  7. 10
  8. 5
  9. (10, 4)
  10. (9, 11)
  11. Fourth quadrant
  12. Fourth quadrant
  13. 15
  14. 15
  15. (9, 4)
  16. (14, 5)
  17. 17
  18. 25
  19. 20
  20. 5
  21. Fourth quadrant
  22. (3, 12)
  23. (7, 9)
  24. 10
  25. (7, 5)
  26. (8, 11)
  27. First quadrant
  28. Second quadrant
  29. 5
  30. (12, 5)
  31. Second quadrant
  32. 10
  33. 25
  34. 15
  35. 17
  36. (4, 16)
  37. Fourth quadrant
  38. (8, 12)
  39. Fourth quadrant
  40. 15

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